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Proof step 41 from proof inv-read-gblock-nodes (previous step)

# lpt0 = # avol, # lpt = # avol, # gndx = # lax, LEB_SIZE = n0 + # buf1, avol[m5] = mapped(buf1), m < LEB_SIZE, m5 < # avol, abs-nodes(buf1, gndx, lax, true), awbuf-inv(avol, bleb), buf-ro-rw-mode(isbuf, bleb, lpt0, avol), bufs-log-only(bleb, log0, lpt0), lpt-free-unref(lpt), lpt-leb-size(lpt), lpt-ram-flash(lpt0, lpt, log0), # buf1 ≤ LEB_SIZE, ∃ gndx1, gndx3, lax1, lax2, buf0, buf2. ax = ax1 + lax1.to-adr(m5) ∧ gndx0 = gndx2 + gndx1 ∧ buf1 = buf0 + buf2 ∧ # buf0 = m ∧ abs-nodes(buf0, gndx1, lax1, false) ∧ abs-nodes(buf2, # buf0, gndx3, lax2, true) ∧ (false → gndx3 = [] ∧ lax2 = []), ¬ m + NODE_HEADER_SIZE ≤ LEB_SIZE ∨ isempty(buf1 + mkempbuf(n0), m, NODE_HEADER_SIZE) ⊦ ∃ gndx1, lax0, buf, buf0. ax = ax1 + lax0.to-adr(m5) ∧ gndx0 = gndx2 + gndx1 ∧ buf1 = buf + buf0 ∧ # buf = m ∧ abs-nodes(buf, gndx1, lax0, false) ∧ abs-nodes(buf0, # buf, [], [], true)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 42:
# lpt = # avol, # lpt0 = # avol, # gndx0 = # lax2, # gndx3 = # lax1, LEB_SIZE = n0 + # buf0 + # buf, avol[m5] = mapped(buf0 + buf), m5 < # avol, abs-nodes(buf0, gndx3, lax1, false), abs-nodes(buf, # buf0, gndx0, lax2, true), awbuf-inv(avol, bleb), buf-ro-rw-mode(isbuf, bleb, lpt0, avol), bufs-log-only(bleb, log0, lpt0), lpt-free-unref(lpt), lpt-leb-size(lpt), lpt-ram-flash(lpt0, lpt, log0), # buf0 + # buf ≤ LEB_SIZE, ¬ # buf0 + NODE_HEADER_SIZE ≤ LEB_SIZE ∨ isempty((buf0 + buf) + mkempbuf(n0), # buf0, NODE_HEADER_SIZE) ⊦ # buf + n0 = 0, ∃ buf1, buf2. buf0 + buf = buf1 + buf2 ∧ # buf1 = # buf0 ∧ abs-nodes(buf1, gndx3, lax1, false) ∧ abs-nodes(buf2, # buf1, [], [], true)

Rule argument

Additional information

Used simplifier rules: nat-stuff0: ⊦ n = n0 + n1 → (n0 < n ↔ n1 ≠ 0);%a: ⊦ (lax + lax0) + lax1 = lax + lax0 + lax1; from specification list[laddress-list]% ⊦ #(lax + lax0) = # lax + # lax0; (s)% ⊦ #(gndx + gndx0) = # gndx + # gndx0; (s)%abs-nodes-elems-adr-length: ⊦ abs-nodes(buf, gndx, lax, weak) → # gndx = # lax; (forward) from specification abs-list[encoding-group-node]%abs-nodes-elems-adr-length-h: ⊦ abs-nodes(buf, m, gndx, lax, weak) → # gndx = # lax; (forward) from specification abs-list[encoding-group-node]%a: ⊦ (gndx + gndx0) + gndx1 = gndx + gndx0 + gndx1; from specification list[group-store]% ⊦ gndx + gndx0 = gndx + gndx1 ↔ gndx0 = gndx1; (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]% ⊦ lax0.to-adr(n) = lax1.to-adr(n) ↔ lax0 = lax1; (s)% ⊦ ax + ax0 = ax + ax1 ↔ ax0 = ax1; (s)%c: ⊦ m + n = n + m; from specification nat-basic%⊦ abs-nodes(buf, m, gndx, lax0, true) → (abs-nodes(buf, m, gndx0, lax1, true) ↔ gndx = gndx0 ∧ lax0 = lax1); (s)%⊦ abs-nodes(buf0, gndx, lax0, false) → ( abs-nodes(buf0 + buf1, gndx0, lax1, boolvar1) ↔ (∃ gndx1, lax2. gndx0 = gndx + gndx1 ∧ lax1 = lax0 + lax2 ∧ abs-nodes(buf1, # buf0, gndx1, lax2, boolvar1))); (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ #(buf + buf0) = # buf + # buf0; (s)